Ethylene-based polymers and processes to make the same

ABSTRACT

A composition comprising an ethylene-based polymer, which comprises the following properties: a) (Mw(abs)/Mw(conv)−2.00)*(100,000 g/mol/Mw(abs))*CDF?IR #191 (MW≤10,000 g/mol)≥0.030; and b) a melt index (I2) from 0.30 to 2.50 g/10 min.

REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of U.S. Application No. 62/338,283, filed on May 18, 2016, and incorporated herein by reference.

BACKGROUND OF THE INVENTION

Blown film production lines are typically limited in output by bubble stability. Blending Linear Low Density Polyethylene (LLDPE) with Low Density Polyethylene (LDPE) increases bubble stability, in part, due to the higher melt strength (MS) of the LDPE, and the increase in MS helps provide for an increase in film output. However, high MS resins typically have reduced the optics and toughness of the film. There is a need for new ethylene-based polymers, such as LDPEs, that provide an optimized balance of melt strength and blown film properties. LDPE polymers are disclosed in the following references: WO 2010/042390, WO 2010/144784, WO 2011/019563, WO 2012/082393, WO 2006/049783, WO 2009/114661, WO 2014/190039, WO 2014/190041, WO 2014/190036, WO 2014/179469, WO 2015/094566, US 2008/0125553, US 2014/0316096, US 2014/0316094, US 2014/0288257, US 2015/0274856, U.S. Pat. Nos. 7,741,415, 8,871,876, 8,415,422, 8,871,887, 8,916,667, 9,243,087, 9,068,032 and EP 2239283B1. However, such polymers do not provide an optimized balance of high MS, high blown film maximum output, and excellent film properties, as discussed herein. Thus, as discussed, there remains a need for new ethylene-based polymers, such as LDPEs, that have an optimized balance of melt strength, polymer processing, film output and film properties. These needs and others have been met by the following invention.

SUMMARY OF THE INVENTION

A composition comprising an ethylene-based polymer, which comprises the following properties:

-   -   a) (Mw(abs)/Mw(conv)−2.00)*(100,000 g/mol/Mw(abs))*CDF_(IR)         (MW≤10,000 g/mol)≥0.030; and b) a melt index (I2) from 0.30 to         2.50 g/10 min.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a chromatogram for the CDF_(IR) determination of Example 1.

FIG. 2 depicts a chromatogram for the CDF_(LS) determination of Example 1.

FIG. 3 depicts a chromatogram for the CDF_(DV) determination of Example 1.

FIG. 4 depicts a block diagram of the polymerization system used to produce the ethylene-based polymers (LDPE) of Examples 1 and 2.

FIG. 5 depicts the “peak melt strength as a function of melt index” for the inventive examples and comparative examples.

DETAILED DESCRIPTION

Novel ethylene-based polymers, such as LDPEs, were developed with an optimized balance of high melt strength, improved blown film maximum output, and excellent film properties. The high melt strength allows an increase in the processability and output of the inventive polymers and blends containing the same.

As discussed above, a composition comprising an ethylene-based polymer, which comprises the following properties:

-   -   a) (Mw(abs)/Mw(conv)−2.00)*(100,000 g/mol/Mw(abs))*CDF_(IR)         (MW≤10,000 g/mol)≥0.030; and b) a melt index (I2) from 0.30 to         2.50 g/10 min.

The composition may comprise a combination of two or more embodiments as described herein. The ethylene-based polymer may comprise a combination of two or more embodiments as described herein.

In one embodiment, the ethylene-based polymer is a LDPE. A LDPE is known in the art, and refers to an ethylene homopolymer prepared using a free-radical, high pressure (≥100 MPa (for example, 100-400 MPa)) polymerization.

In one embodiment, the ethylene-based polymer has a “(Mw(abs)/Mw(conv)−2.00)*(100,000 g/mol/Mw(abs))*CDF_(IR) (MW<10,000 g/mol)”≤0.060, or ≤0.058, or ≤0.056, or ≤0.054, or ≤0.052.

In one embodiment, the ethylene-based polymer has a “(Mw(abs)/Mw(conv)−2.00)*(100,000 g/mol/Mw(abs))*CDF_(IR) (MW<10,000 g/mol)” from 0.030 to 0.060, or from 0.030 to 0.058, or from 0.030 to 0.056, or from 0.030 to 0.054, or from 0.030 to 0.052.

In one embodiment, the ethylene-based polymer has a CDF_(IR) (at MW≤10,000 g/mol)≥0.140, or ≥0.150, or ≥0.152, or ≥0.154. In one embodiment, the ethylene-based polymer has a CDF_(IR) (at MW≤10,000 g/mol)≤0.400, or ≤0.350, or ≤0.300, or ≤0.250.

In one embodiment, the ethylene-based polymer has a CDF_(LS) (at MW≥750,000 g/mol)≥0.400, or ≥0.410, or ≥0.420. In a further embodiment, the ethylene-based polymer is a LDPE. In one embodiment, the ethylene-based polymer has a CDF_(LS) (at MW≥750,000 g/mol)≤0.650, or ≤0.620, or ≤0.600.

In one embodiment, the ethylene-based polymer has a CDF_(DV) (at MW≥1, 200,000 g/mol)≥0.020, or ≥0.022, or ≥0.024, or ≥0.026, or ≥0.028. In one embodiment, the ethylene-based polymer has a CDF_(DV) (at MW≥1, 200,000 g/mol)≤0.150, or ≤0.100, or ≤0.080. In one embodiment, the ethylene-based polymer has an Intrinsic Viscosity (Absolute by viscometer on-line by GPC) or IV (bulk) from 0.90 to 1.20, or from 0.92 to 1.10.

In one embodiment, the ethylene-based polymer has a Mw(abs)/Mw(conv) ratio≥2.50, or ≥2.55, or ≥2.60, or ≥2.62. In one embodiment, the ethylene-based polymer has a Mw(abs)/Mw(conv) ratio from 2.50 to 5.00, further from 2.50 to 4.50, further from 2.50 to 4.00, further from 2.50 to 3.50, and further from 2.50 to 3.00.

In one embodiment, the polymer has a GPC Mw(conv) from 75,000 to 250,000 g/mol, or from 100,000 to 200,000 g/mol, or from 100,000 to 175,000 g/mol, or 100,000 to 150,000 g/mol, or from 110,000 to 150,000 g/mol. In one embodiment, the polymer has a Mw(conv)/Mn(conv)≥7.5, or ≥8.0, or ≥8.5. In one embodiment, the polymer has a Mw(conv)/Mn(conv)≤14.0, or ≤12.0, or ≤10.0. In one embodiment, the polymer has a Mw(conv)/Mn(conv) from 7.5 to 14.0, or from 8.0 to 12.0, or from 8.5 to 10.0. In one embodiment, the polymer has a Mn(conv) from 10,000 to 18,000 g/mol, or from 12,000 to 16,000 g/mol, or from 13,000 to 16,000 g/mol. In one embodiment, the ethylene-based polymer has a z-average molecular weight Mz(conv)≥450,000 g/mol, or ≥480,000 g/mol, or ≥500,000 g/mol. In one embodiment, the ethylene-based polymer has a z-average molecular weight Mz(conv)≤700,000 g/mol, or ≤650,000 g/mol.

In one embodiment, the polymer has a Mw(abs) from 220,000 to 480,000 g/mol, or from 240,000 to 460,000 g/mol, or from 260,000 to 440,000 g/mol, and or from 280,000 to 420,000 g/mol. In one embodiment, the polymer has a Mz(abs) from 3,000,000 to 6,000,000 g/mol, or from 3,500,000 to 5,500,000 g/mol, or from 4,000,000 to 5,000,000 g/mol, or from 4,200,000 to 5,000,000 g/mol. In one embodiment, the ethylene-based polymer has a Mz(abs)/Mw(abs) from 9.5 to 17.5, or from 10.0 to 17.0, or from 10.5 to 16.5, or from 11.0 to 16.0.

In one embodiment, the ethylene-based polymer has a gpcBR value from 2.00 to 4.00, or from 2.20 to 3.80, or from 2.50 to 3.50. In one embodiment, the ethylene-based polymer has a LCBf value from 2.00 to 4.60, or from 2.10 to 4.40, or from 2.30 to 4.20, or from 2.50 to 4.00.

In one embodiment, the ethylene-based polymer has a melt viscosity, at 0.1 rad/s and 190° C., ≥8,000 Pa·s, or ≥9,000 Pa·s. In one embodiment, the ethylene-based polymer has a melt viscosity, at 0.1 rad/s and 190° C., ≤35,000 Pa·s, or ≤30,000 Pa·s, or ≤25,000 Pa·s. In one embodiment, the ethylene-based polymer has a melt viscosity ratio (V0.1/V100), at 190° C., ≥18, or ≥20, or ≥22. In one embodiment, the ethylene-based polymer has a viscosity ratio (V0.1/V100, at 190° C.) from 18 to 40, or from 19 to 39, or from 20 to 38.

In one embodiment, the ethylene-based polymer has a tan delta (at 0.1 rad/s at 190° C.)≤3.20, or ≤3.00, or ≤2.80, or ≤2.60. In one embodiment, the ethylene-based polymer has a tan delta (measured at 0.1 rad/s at 190° C.) from 1.00 to 3.20, or from 1.20 to 3.10, or from 1.40 to 3.00, or from 1.50 to 2.80.

In one embodiment, the ethylene-based polymer has a peak melt strength (MS)>10.0 cN, or ≥11.0 cN. In one embodiment, the ethylene-based polymer has a peak melt strength, at 190° C., greater than “−2.5*(I₂ at 190° C.)+15.5 cN.” Here, the unit of the “−2.5 coefficient” is as follows: “(cN)/(g/10 min)”. In one embodiment, the ethylene-based polymer has a peak melt strength, at 190° C., greater than “−2.5*(I₂ at 190° C.)+15.5 cN” and less than “−2.5*(I₂ at 190° C.)+20.5 cN.”

In one embodiment, the ethylene-based polymer has a melt index (I2)≥0.35 g/10 min, or ≥0.40 g/10 min, or ≥0.50 g/10 min. In one embodiment, the ethylene-based polymer has a melt index (I2)≤2.20 g/10 min, or ≤2.00 g/10 min, or ≤1.80 g/10 min, or ≤1.60 g/10 min. In one embodiment, the ethylene-based polymer has a melt index (I2) from 0.30 to 2.20 g/10 min, or from 0.35 to 2.00 g/10 min, or from 0.40 to 1.80 g/10 min, or from 0.45 to 1.60 g/10 min.

In one embodiment, the ethylene-based polymer has a density from 0.910 to 0.940 g/cc, or from 0.915 to 0.930 g/cc, or from 0.916 to 0.925 g/cc, or from 0.917 to 0.923 g/cc, or from 0.918 to 0.922 g/cc, or from 0.919 to 0.921 g/cc (1 cc=1 cm³). In one embodiment, the ethylene-based polymer has a % hexane extractables from 1.0 to 4.0 wt %, or from 1.5 to 3.0 wt %, or from 2.0 to 2.5 wt %, based on the weight of the polymer.

In one embodiment, the ethylene-based polymer has ≥0.1 amyl groups (C5) per 1000 total carbon atoms, or ≥0.2 amyl (C5) groups (branches) per 1000 total carbon atoms, or ≥0.5 amyl groups per 1000 total carbon atoms, or ≥1.0 amyl groups per 1000 total carbon atoms, or ≥1.5 amyl groups per 1000 total carbon atoms, or ≥2.0 amyl groups per 1000 total carbon atoms, or ≥2.2 amyl groups per 1000 total carbon atoms, in which the amyl group is equivalent to the C5 group, and is measured by ¹³C NMR. In one embodiment, the ethylene-based polymer has ≤4.0 amyl groups (C5) per 1000 total carbon atoms, or ≤3.5 amyl (C5) groups (branches) per 1000 total carbon atoms, or ≥0.5 amyl groups per 1000 total carbon atoms, or ≥1.0 amyl groups per 1000 total carbon atoms.

In one embodiment, the ethylene-based polymer has from 0.1 to 2.5 C1 (methyl groups) per 1000 total carbon atoms, or from 0.2 to 2.0 C1 (methyl) per 1000 total carbon atoms, or from 0.5 to 1.5 C1 (methyl) per 1000 total carbon atoms, as determined by ¹³C NMR. In one embodiment, the ethylene-based polymer has from 4.0 to 6.0 of 1,3 diethyl branches per 1000 total carbon atoms, or from 4.1 to 5.0 of 1,3 diethyl branches per 1000 total carbon atoms, or from 4.2 to 4.7 of 1,3 diethyl branches per 1000 total carbon atoms, as determined by ¹³C NMR.

In one embodiment, the ethylene-based polymer has from 1.00 to 3.00 C2 on the quaternary carbon atom per 1000 total carbon atoms, or from 1.40 to 2.00 C2 on the quaternary carbon atom per 1000 total carbon atoms, or from 1.45 to 1.70 C2 on the quaternary carbon atom per 1000 total carbon atoms, as determined by ¹³C NMR. In one embodiment, the ethylene-based polymer has from 0.05 to 0.15 vinyls per 1000 total carbon atoms, or from 0.08 to 0.14 vinyls per 1000 total carbon atoms, or from 0.10 to 0.13 vinyls per 1000 total carbon atoms, as determined by 1H NMR.

In one embodiment, the ethylene-based polymer has from 0.03 to 0.06 cis and trans groups (vinylene) per 1000 total carbon atoms, and or from 0.04 to 0.06 cis and trans per 1000 total carbon atoms, as determined by 1H NMR. In one embodiment, the ethylene-based polymer has from 0.10 to 0.40 vinylidene per 1000 total carbon atoms, or from 0.10 to 0.30 vinylidene per 1000 total carbon atoms, as determined by 1H NMR.

In one embodiment, the ethylene-based polymer has a crystallization temperature from 96.0° C. to 100.0° C., or from 96.5° C. to 99.0° C. In one embodiment, the ethylene-based polymer has a melting point (Tm, DSC) from 106° C. to 115° C., or from 107° C. to 112° C., or from 108° C. to 110° C.

In one embodiment, the ethylene-based polymer is formed in a high pressure (P≥100 MPa), free radical polymerization process. In a further embodiment, the ethylene-based polymer is a LDPE.

In one embodiment, the ethylene-based polymer is present at ≥10 weight percent, based on the weight of the composition. In one embodiment, the ethylene-based polymer is present in an amount from 10 to 50 weight percent, or from 20 to 40 weight percent, based on the weight of the composition. In one embodiment, the ethylene-based polymer is present in an amount from 60 to 90 weight percent, or from 65 to 85 weight percent, based on the weight of the composition. In one embodiment, the ethylene-based polymer is present in an amount from 1 to 10 weight percent, or from 1.5 to 5 weight percent, based on the weight of the composition.

In one embodiment, the composition further comprises another polymer different from the ethylene-based polymer. In one embodiment, the composition further comprises another ethylene-based polymer that differs in one or more properties, such as density, melt index, comonomer, comonomer content, etc., from the inventive ethylene-based polymer. Suitable other ethylene-based polymers include, but are not limited to, DOWLEX Polyethylene Resins (LLDPEs), TUFLIN Linear Low Density Polyethylene Resins, ELITE or ELITE AT Enhanced Polyethylene Resins, or INNATE Precision Packaging Resins (all available from The Dow Chemical Company), high density polyethylenes (d≥0.96 g/cc), medium density polyethylenes (density from 0.935 to 0.955 g/cc), EXCEED polymers and ENABLE polymers (both from ExxonMobil), LDPE, and EVA (ethylene vinyl acetate).

In one embodiment, the composition further comprises a propylene-based polymer. Suitable propylene-based polymers include polypropylene homopolymers, propylene/α-olefin interpolymers, and propylene/ethylene interpolymers. In one embodiment, the composition further comprises a heterogeneously branched ethylene/α-olefin interpolymer, and preferably such copolymer. In one embodiment, the heterogeneously branched ethylene/α-olefin interpolymer, and preferably a heterogeneously branched ethylene/α-olefin copolymer, has a density from 0.89 to 0.94 g/cc, or from 0.90 to 0.93 g/cc. In a further embodiment, the composition comprises 1 to 99 wt %, or from 15 to 85 wt %, or from 10 to 50 wt % of the inventive ethylene-based polymer, based on the weight of the composition. In one embodiment, the composition comprises from 10 to 80 wt %, or from 20 to 80 wt %, or from 50 to 80 wt % of an inventive ethylene-based polymer, based on the weight of the composition. In a further embodiment, the composition further comprises a LLDPE. In one embodiment, the ethylene-based polymer is a low density polyethylene (LDPE).

In one embodiment, the composition comprises less than 5 ppm, further less than 2 ppm, further less than 1 ppm, and further less than 0.5 ppm sulfur, based on the weight of the composition. In one embodiment, the composition does not contain sulfur. In one embodiment, the composition comprises less than 5 ppm, further less than 2 ppm, further less than 1 ppm, and further less than 0.5 ppm of an azide, based on the weight of the composition. In one embodiment, the composition does not contain an azide.

The invention also provides an article comprising at least one component formed from an inventive composition. In a further embodiment, the article is a film. In a further embodiment, the film has Dart value≥200 g, or ≥210 g, or ≥220 g, or ≥230 g, or ≥240 g, at a film thickness of 2.00 mil±0.15 mil, as determined by ASTM D 1709-09 (reported by method A). In another embodiment, the article is a coating.

The invention also provides a process for forming an ethylene-based polymer of any of the previous embodiments, the process comprising polymerizing a mixture comprising ethylene, in at least one tubular reactor. The invention also provides a process for forming an inventive ethylene-based polymer of any of the previous embodiments, the process comprising polymerizing a mixture comprising ethylene, in a combination of at least one tubular reactor and at least one autoclave reactor.

An inventive composition may comprise a combination of two or more embodiments as described herein. An inventive ethylene-based polymer may comprise a combination of two or more embodiments as described herein. An inventive LDPE may comprise a combination of two or more embodiments as described herein. An inventive article may comprise a combination of two or more embodiments as described herein. An inventive film may comprise a combination of two or more embodiments as described herein. An inventive process may comprise a combination of two or more embodiments as described herein.

Process

For producing an inventive ethylene-based polymer, including an inventive LDPE, a high pressure, free-radical initiated polymerization process is typically used. Typically, a jacketed tube is used as a reactor, which has one or more reaction zones. Suitable, but not limiting, reactor lengths may be from 100 to 3000 meters (m), or from 1000 to 2000 meters. The beginning of a reaction zone for the reactor is typically defined by the side injection of initiator of the reaction, ethylene, chain transfer agent (or telomer), as well as any combination thereof. A high pressure process can be carried out in tubular reactors, having one or more reaction zones, or in a combination of autoclave and tubular reactors, each comprising one or more reaction zones.

A chain transfer agent can be used to control molecular weight. In a preferred embodiment, one or more chain transfer agents (CTAs) are added to an inventive polymerization process. Typical CTA's that can be used include, but are not limited to, propylene, propionaldehyde, isobutane, methylethyl ketone, n-butane and 1-butene. In one embodiment, the amount of CTA used in the process is from 0.03 to 10 weight percent of the total reaction mixture. Ethylene used for the production of the ethylene-based polymer may be purified ethylene, which is obtained by removing impurities from a loop recycle stream, or by using a reaction system configuration, such that only fresh ethylene is used for making the inventive polymer. It is not typical that only purified ethylene is required to make the ethylene-based polymer. In such cases ethylene from the recycle loop may be used. In one embodiment, the ethylene-based polymer is a LDPE.

Additives

An inventive composition may comprise one or more additives. Additives include, but are not limited to, stabilizers, plasticizers, antistatic agents, pigments, dyes, nucleating agents, fillers, slip agents, fire retardants, processing aids, smoke inhibitors, viscosity control agents and anti-blocking agents. The polymer composition may, for example, comprise less than 10 percent (by the combined weight) of one or more additives, based on the weight of the inventive polymer composition. In one embodiment, the polymers of this invention are treated with one or more stabilizers, for example, antioxidants, such as IRGANOX 1010, IRGANOX 1076 and IRGAFOS 168 (Ciba Specialty Chemicals; Glattbrugg, Switzerland). The polymers may be treated with one or more stabilizers before extrusion or other melt processes. Blends and mixtures of the inventive polymer with other polymers may be performed. Suitable polymers for blending include natural and synthetic polymers.

Applications

The polymers of this invention may be employed in a variety of conventional thermoplastic fabrication processes to produce useful articles, including, but not limited to, monolayer and multilayer films; molded articles, such as blow molded, injection molded, or rotomolded articles; coatings (for example, extrusion coatings); fibers; and woven or nonwoven fabrics. An inventive polymer may be used in a variety of films, including but not limited to, food packaging, consumer, industrial, agricultural (applications or films), lamination films, fresh cut produce films, meat films, cheese films, candy films, clarity shrink films, collation shrink films, stretch films, silage films, greenhouse films, fumigation films, liner films, stretch hood, heavy duty shipping sacks, pet food, sandwich bags, sealants, and diaper backsheets. An inventive polymer is also useful in other direct end-use applications. An inventive polymer may be used for wire and cable coating operations, in sheet extrusion for vacuum forming operations, and forming molded articles, including the use of injection molding, blow molding processes, or rotomolding processes.

Definitions

The term “polymer,” as used herein, refers to a polymeric compound prepared by polymerizing monomers, whether of the same or a different type. The generic term polymer thus embraces the term homopolymer (employed to refer to polymers prepared from only one type of monomer, with the understanding that low amounts of impurities (for example, low amounts (e.g., ≤1.0 wt %, further ≤0.5 wt %, further ≤0.3 wt %) of CTA) can be incorporated into the polymer structure), and the term interpolymer as defined hereinafter. Impurities may be incorporated into and/or within a polymer.

The term “interpolymer,” as used herein, refers to polymers prepared by the polymerization of at least two different types of monomers. The generic term interpolymer includes copolymers (employed to refer to polymers prepared from two different types of monomers), and polymers prepared from more than two different types of monomers.

The term “ethylene-based polymer,” as used herein, refers to a polymer that comprises a majority amount of polymerized ethylene monomer (based on weight of the polymer), and, optionally, may contain at least one comonomer.

The term “propylene-based polymer,” as used herein, refers to a polymer that comprises a majority amount of polymerized propylene monomer (based on weight of the polymer) and, optionally, may comprise at least one comonomer.

The term “composition,” as used herein, includes a mixture of materials which comprise the composition, as well as reaction products and decomposition products formed from the materials of the composition.

The terms “blend” or “polymer blend,” as used, refers to a mixture of two or more polymers. A blend may or may not be miscible (not phase separated at the molecular level). A blend may or may not be phase separated. A blend may or may not contain one or more domain configurations, as determined from transmission electron spectroscopy, light scattering, x-ray scattering, and other methods known in the art. The blend may be effected by physically mixing the two or more polymers on the macro level (for example, blending resins) or the micro level (for example, simultaneous forming within the same reactor).

The terms “comprising,” “including,” “having,” and their derivatives, are not intended to exclude the presence of any additional component, step or procedure, whether or not the same is specifically disclosed. In order to avoid any doubt, all compositions claimed through use of the term “comprising” may include any additional additive, adjuvant, or compound, whether polymeric or otherwise, unless stated to the contrary. In contrast, the term, “consisting essentially of” excludes from the scope of any succeeding recitation any other component, step or procedure, excepting those that are not essential to operability. The term “consisting of” excludes any component, step or procedure not specifically delineated or listed.

Test Methods

Density—

Samples for density measurements were prepared according to ASTM D 4703-10 Annex A1 Procedure C. Approximately 7 g of sample was placed in a “2″×2″×135 mil thick” mold, and this was pressed at 374° F. (190° C.) for six minutes at 3,000 lb_(f). Then the pressure was increased to 30,000 lb_(f) for four minutes. This was followed by cooling at 15° C. per minute, at 30,000 lb_(f), to approximately a temperature of 40° C. The “2”×2″×135 mil″ polymer sample (plaque) was then removed from the mold, and three samples were cut from the plaque with a ½″×1″ die cutter. Density measurements were made within one hour of sample pressing, using ASTM D792-08, Method B. Density was reported as an average of three measurements.

Melt Index—

Melt index (MI), or I2, was measured in accordance with ASTM D 1238-10, Condition 190° C./2.16 kg, Procedure B, and reported in g/10 min.

Hexane Extractables

Polymer pellets (from the polymerization pelletization process, without further modification; approximately 2.2 grams per one “1-inch by 1-inch” square film) were pressed in a Carver Press at a thickness of 3.0-4.0 mils. The pellets were pressed at 190° C. for 3 minutes, at 40,000 lb_(f). Non-residue gloves (PIP* CleanTeam* CottonLisle Inspection Gloves, Part Number: 97-501) were worn to prevent contamination of the film with residual oils from the hands of the operator. Each film was trimmed to a “1-inch by 1-inch” square, and weighed (2.5±0.05 g). The films were extracted for two hours, in a hexane vessel, containing about 1000 ml of hexane, at 49.5±0.5° C., in a heated water bath. The hexane was an “isomeric hexanes” mixture (for example, Hexanes (Optima), Fisher Chemical, high purity mobile phase for HPLC and/or extraction solvent for GC (gas chromatography) applications). After two hours, the films were removed, rinsed in clean hexane, and dried in a vacuum oven (80±5° C.) at full vacuum (ISOTEMP Vacuum Oven, Model 281A, at approximately 30 inches Hg) for two hours. The films were then placed in a desiccator, and allowed to cool to room temperature for a minimum of one hour. The films were then reweighed, and the amount of mass loss due to extraction in hexane was calculated. This method is based on 21 CRF 177.1520 (d)(3)(ii), with one deviation from FDA protocol by using the “isomeric hexanes” instead of “n-hexane.” The average of three measurements were reported.

Nuclear Magnetic Resonance (¹³C NMR)

Each sample was prepared by adding approximately “3 g of a 50/50 mixture of tetrachloroethane-d2/orthodichlorobenzene, containing 0.025 M Cr(AcAc)₃,” to a “0.25 to 0.40 g polymer sample,” in a 10 mm NMR tube. The sample was then dissolved and homogenized by heating the tube, and its contents to 150° C., using a heating block and heat gun. Each dissolved sample was visually inspected to ensure homogeneity. All data were collected using a Bruker 400 MHz spectrometer, equipped with a Bruker Dual DUL high-temperature CryoProbe. The data was acquired using a six second pulse repetition delay, 90-degree flip angles, and inverse gated decoupling, with a sample temperature of 120° C. All measurements were made on non-spinning samples in locked mode. The ¹³C NMR chemical shifts were internally referenced to the EEE triad at 30.0 ppm. The C6+ value was a direct measure of C6+ branches in LDPE, where the long branches were not distinguished from chain ends. The 32.2 ppm peak, representing the third carbon from the end of all chains or branches of six or more carbons, was used to determine the C6+ value. Other peaks of interest are listed in Table A.

TABLE A Branch Type Peak(s) integrated Identity of the integrated carbon peak(s) 1,3 diethyl About 10.5 to 1,3 diethyl branch methyls 11.5 ppm C1 About 19.75 to C1, methyls 20.50 ppm C2 on Quat About 7.7 to 8.6 2 ethyl groups on a quaternary carbon Carbon ppm C4 About 23.3 to Second CH₂ in a 4-carbon branch, 23.5 ppm counting the methyl as the first C C5 About 32.60 to Third CH₂ in a 5-carbon branch, 32.80 ppm counting the methyl as the first C Nuclear Magnetic Resonance (¹H NMR)

Each sample was prepared by adding approximately 130 mg of sample to “3.25 g of 50/50, by weight, tetrachlorethane-d2/perchloroethylene” with 0.001 M Cr(AcAc)₃, in a NORELL 1001-7, 10 mm NMR tube. The sample was purged by bubbling N₂ through the solvent, via a pipette inserted into the tube, for approximately five minutes, to prevent oxidation. The tube was capped, sealed with TEFLON tape, and then soaked at room temperature, overnight, to facilitate sample dissolution. The sample was heated and vortexed at 115° C. to ensure homogeneity.

The ¹H NMR was performed on a Bruker AVANCE 400 MHz spectrometer, equipped with a Bruker Dual DUL high-temperature CryoProbe, and at a sample temperature of 120° C. Two experiments were run to obtain spectra, a control spectrum to quantitate the total polymer protons, and a double presaturation experiment, which suppressed the intense polymer backbone peaks, and enabled high sensitivity spectra for quantitation of the end-groups. The control was run with ZG pulse, 16 scans, AQ 1.64 s, D1 14 s. The double presaturation experiment was run with a modified pulse sequence, 100 scans, AQ 1.64 s, presaturation delay 1 s, relaxation delay 13 s.

The signal from residual ¹H in TCE-d2 (at 6.0 ppm) was integrated, and set to a value of 100, and the integral from 3 to −0.5 ppm was used as the signal from the whole polymer in the control experiment. For the presaturation experiment, the TCE signal was also set to 100, and the corresponding integrals for unsaturation (vinylene (cis and trans) at about 5.40 to 5.60 ppm, trisubstituted at about 5.16 to 5.35 ppm, vinyl at about 4.95 to 5.15 ppm, and vinylidene at about 4.70 to 4.90 ppm) were obtained.

Melt Strength

Melt strength measurements were conducted on a Gottfert Rheotens 71.97 (Göettfert Inc.; Rock Hill, S.C.), attached to a Gottfert Rheotester 2000 capillary rheometer. The melted sample (about 25 to 30 grams) was fed with a Göettfert Rheotester 2000 capillary rheometer, equipped with a flat entrance angle (180 degrees) of length of 30 mm, diameter of 2.0 mm, and an aspect ratio (length/diameter) of 15. After equilibrating the samples at 190° C. for 10 minutes, the piston was run at a constant piston speed of 0.265 mm/second. The standard test temperature was 190° C. The sample was drawn uniaxially to a set of accelerating nips, located 100 mm below the die, with an acceleration of 2.4 mm/s². The tensile force was recorded as a function of the take-up speed of the nip rolls. Melt strength was reported as the peak or maximum plateau force (cN). The following conditions were used in the melt strength measurements: plunger speed=0.265 mm/second; wheel acceleration=2.4 mm/s²; capillary diameter=2.0 mm; capillary length=30 mm; and barrel diameter=12 mm. The peak melt strength is the maximum melt strength recorded.

Dynamic Mechanical Spectroscopy (DMS)

Resins were compression-molded into “3 mm thick×1 inch” circular plaques at 350° F., for 6.5 minutes, under 20,000 lb_(f), in air. The sample was then taken out of the press, and placed on the counter to cool. A constant temperature frequency sweep was performed, using a TA Instruments “Advanced Rheometric Expansion System (ARES),” equipped with 25 mm (diameter) parallel plates, under a nitrogen purge. The sample was placed on the plate, and allowed to melt for five minutes at 190° C. The plates were then closed to a gap of 2 mm, the sample trimmed (extra sample that extends beyond the circumference of the “25 mm diameter” plate was removed), and then the test was started. The method had an additional five minute delay built in, to allow for temperature equilibrium. The experiments were performed at 190° C., over a frequency range of 0.1 to 100 rad/s. The strain amplitude was constant at 10%. The complex viscosity η*, tan (δ) or tan delta, viscosity at 0.1 rad/s (V0.1), the viscosity at 1 rad/s (V1), the viscosity at 10 rad/s (V10), the viscosity at 100 rad/s (V100), and the viscosity ratio (V0.1/V100) were measured.

Triple Detector Gel Permeation Chromatography (TDGPC)

The chromatographic system consisted of a PolymerChar GPC-IR (Valencia, Spain) high temperature GPC chromatograph, equipped with an internal IR5 infra-red detector (IR5) coupled to a Precision Detectors (Now Agilent Technologies) 2-angle laser light scattering (LS) detector Model 2040, and followed by a PolymerChar 4-capillary viscosity detector (three detectors in series). For all light scattering measurements, the 15 degree angle was used for measurement purposes. The autosampler oven compartment was set at 160° Celsius, and the column compartment was set at 150° Celsius. The columns used were four, Agilent “Mixed A” columns, each 30 cm, and each packed with 20-micron linear mixed-bed particles. The chromatographic solvent used was 1,2,4-trichlorobenzene, which contained 200 ppm of butylated hydroxytoluene (BHT). The solvent source was nitrogen sparged. The injection volume was 200 microliters, and the flow rate was 1.0 milliliters/minute.

Calibration of the GPC column set was performed with 21 narrow molecular weight distribution, polystyrene standards with molecular weights ranging from 580 to 8,400,000 g/mol. These standards were arranged in 6 “cocktail” mixtures, with at least a decade of separation between individual molecular weights. The standards were purchased from Agilent Technologies. The polystyrene standards were prepared at “0.025 grams in 50 milliliters of solvent” for molecular weights equal to, or greater than, 1,000,000, g/mol, and at “0.05 grams in 50 milliliters of solvent” for molecular weights less than 1,000,000 g/mol. The polystyrene standards were dissolved at 80 degrees Celsius, with gentle agitation, for 30 minutes. The polystyrene standard peak molecular weights (IR 5 detector) were converted to polyethylene molecular weights using Equation 1 (as described in Williams and Ward, J. Polym. Sci., Polym. Let., 6, 621 (1968)): M _(polyethylene) =A×(M _(polystyrene))^(B)  (EQN 1), where M is the molecular weight, A has a value of 0.4315, and B is equal to 1.0. A fifth order polynomial was used to fit the respective polyethylene-equivalent calibration points. A small adjustment to A (from approximately 0.415 to 0.44) was made to correct for column resolution and band-broadening effects, such that NIST standard NBS 1475 was obtained at 52,000 g/mol (Mw).

The total plate count of the GPC column set was performed with EICOSANE (prepared at 0.04 g in 50 milliliters of “TCB stabilized solvent,” and dissolved for 20 minutes with gentle agitation.) The plate count (Equation 2) and symmetry (Equation 3) were measured on a 200 microliter injection according to the following equations:

$\begin{matrix} {{{{Plate}\mspace{14mu}{Count}} = {5.54 \star \left( \frac{\left( {RV}_{{Peak}\;{Max}} \right)}{{Peak}\mspace{11mu}{Width}\mspace{11mu}{at}\mspace{11mu} 1\text{/}2\mspace{11mu}{height}} \right)^{2}}},} & \left( {{EQN}\mspace{14mu} 2} \right) \end{matrix}$ where RV is the retention volume in milliliters, the peak width is in milliliters, the peak max is the maximum height of the peak, and ½ height is the ½ height of the peak maximum:

$\begin{matrix} {{{Symmetry} = \frac{\left( {{{Rear}\mspace{14mu}{Peak}\mspace{11mu}{RV}_{{one}\mspace{11mu}{tenth}\mspace{11mu}{height}}} - {RV}_{{Peak}\mspace{11mu}\max}} \right)}{\left( {{RV}_{{Peak}\mspace{11mu}\max} - {{Front}\mspace{14mu}{Peak}\mspace{11mu}{RV}_{{one}\mspace{11mu}{tenth}\mspace{11mu}{height}}}} \right)}},} & \left( {{EQN}\mspace{14mu} 3} \right) \end{matrix}$ where RV is the retention volume in milliliters, and the peak width is in milliliters, “Peak max” is the maximum IR signal height corresponding to an “RV position” on the chromatogram, “One tenth height” 1/10 height of the peak maximum, where “Rear peak” refers to the peak tail at a signal retention volume (at 1/10 height of peak maximum), later than the peak max, and where “Front peak” refers to the peak front at a signal retention volume (at 1/10 height of peak maximum), earlier than the peak max. The plate count for the chromatographic system should be greater than 24,000, and the symmetry should be between 0.98 and 1.22.

Samples were prepared in a semi-automatic manner with the PolymerChar “Instrument Control” Software, wherein the samples were weight-targeted at 2 mg/ml, and the solvent (contained 200 ppm BHT) was added to a pre nitrogen-sparged septa-capped vial, via the PolymerChar high temperature autosampler. Decane (a flow rate marker) was added to each sample (about 5 microliters). The samples were dissolved for two hours at 160° Celsius, under a “low speed” shaking.

IR 5 Chromatogram

The calculations of Mn(conv), Mw(conv), and Mz(conv) were based on the GPC results, using the internal IR5 detector (measurement channel) of the PolymerChar GPC-IR chromatograph, according to Equations 4-6, using PolymerChar GPCOne™ software (version 2013G), the baseline-subtracted IR chromatogram at each equally-spaced data collection point (i), and the polyethylene equivalent molecular weight obtained from the narrow standard calibration curve for the point (i) from Equation 1. Table 4 lists the conventional GPC results for the examples and comparative examples using Equations 4-6, below for the conventional GPC.

$\begin{matrix} {{{Mn}_{({conv})} = \frac{\sum\limits^{i}{IR}_{i}}{\sum\limits^{i}\left( \frac{{IR}_{i}}{M_{{polyethylene}_{i}}} \right)}},} & \left( {{EQN}\mspace{14mu} 4} \right) \\ {{{Mw}_{({conv})} = \frac{\sum\limits^{i}\left( {{IR}_{i} \star M_{{polyethylene}_{i}}} \right)}{\sum\limits^{i}{IR}_{i}}},} & \left( {{EQN}\mspace{14mu} 5} \right) \\ {{Mz}_{({conv})} = {\frac{\sum\limits^{i}\left( {{IR}_{i} \star M_{{polyethylene}_{i}^{2}}} \right)}{\sum\limits^{i}\left( {{IR}_{i} \star M_{{polyethylene}_{i}}} \right)}.}} & \left( {{EQN}\mspace{14mu} 6} \right) \end{matrix}$

In order to monitor the deviations over time, a flowrate marker (decane) was introduced into each sample via a micropump controlled with the PolymerChar GPC-IR system. This flowrate marker (FM, here decane) was used to linearly correct the pump flowrate (Flowrate(nominal)) for each sample, by aligning the RV value of the respective decane peak within the sample (RV(FM Sample)), to that of the decane peak within the narrow standards calibration (RV(FM Calibrated)). Any changes in the time of the decane marker peak were then assumed to be related to a linear-shift in flowrate (Flowrate(effective)) for the entire run. To facilitate the highest accuracy of a RV measurement of the flow marker peak, a least-squares fitting routine was used to fit the peak of the flow marker concentration chromatogram to a quadratic equation. The first derivative of the quadratic equation was then used to solve for the true peak position. After calibrating the system based on a flow marker peak, the effective flowrate (with respect to the narrow standards calibration) was calculated using Equation 7. Processing of the flow marker peak was done via the PolymerChar GPCOne™ Software. Acceptable flowrate correction was such that the effective flowrate should be within +/−2% of the nominal flowrate. Flowrate(effective)=Flowrate(nominal)*(RV(FM Calibrated)/RV(FM Sample))  (EQN 7)

The Systematic Approach for the determination of multi-detector offsets was done in a manner consistent with that published by Balke, Mourey, et. al. (Mourey and Balke, Chromatography Polym. Chpt 12, (1992)) (Balke, Thitiratsakul, Lew, Cheung, Mourey, Chromatography Polym. Chpt 13, (1992)). Alignment of the triple detector log (MW and IV) results (generated from a broad homopolymer polyethylene standard (Mw/Mn=3)), to the narrow standard column calibration results (generated from the narrow standards calibration curve), was done using the PolymerChar GPCOne™ Software.

Light Scattering Chromatogram

The absolute molecular weight data (MWabs) was obtained in a manner consistent with that published by Zimm (Zimm, B. H., J. Chem. Phys., 16, 1099 (1948)) and Kratochvil (Kratochvil, P., Classical Light Scattering from Polymer Solutions, Elsevier, Oxford, N.Y. (1987)), using the PolymerChar GPCOne™ software. The overall injected concentration, used in the determination of the molecular weight, was obtained from the mass detector area and the mass detector constant, derived from a suitable linear polyethylene homopolymer, or one of the polyethylene standards of known weight-average molecular weight (traceable to NBS 1475 homopolymer polyethylene reference sample). The calculated molecular weights (using GPCOne™) were obtained using a light scattering constant, derived from one or more of the polyethylene standards mentioned below, and a refractive index concentration coefficient, dn/dc, of 0.104. Generally, the mass detector response (IR5) and the light scattering constant (determined using GPCOne™) should be determined from a linear standard with a molecular weight in excess of about 50,000 g/mol. Table 5 lists the light scattering GPC results for the examples and comparative examples.

The Equation for Mw(abs) is an area-based result, using the baseline-subtracted 15 degree light scattering signal and the baseline-subtracted IR5 measurement sensor signal (applying the mass and light scattering constants), as determined from GPCOne™ software,

${Mw}_{({abs})} = {\frac{\sum\limits^{i}{LS}_{i}}{\sum\limits^{i}{IR}_{i}} \times {Mass}\mspace{14mu}{Constant}\text{/}{LS}\mspace{11mu}{{constant}.}}$

The equation for Mz(abs) relied on a point-by point determination of the absolute molecular weight derived from the ratio of the baseline-subtracted, 15 degree light scattering signal and the baseline-subtracted, IR5 measurement sensor signal, and factored for the mass constant and light scattering constant, using GPCOne™ software. A straight-line fit was used to extrapolate the absolute molecular weight, where either detector (IR5 or LS) is below approximately 4% relative peak signal height (maximum peak height).

${Mz}_{({abs})} = \frac{\sum\limits^{i}\left( {{IR}_{i} \star M_{{Abs}_{i}^{2}}} \right)}{\sum\limits^{i}\left( {{IR}_{i} \star M_{{Abs}_{i}}} \right)}$ Viscosity Chromatogram

The absolute intrinsic viscosity data (IV(abs)) was obtained using the area of the specific viscosity chromatogram, obtained from the PolymerChar viscometer detector, when calibrated to the known intrinsic viscosity of NBS 1475. The overall injected concentration, used in the determination of the intrinsic viscosity, was obtained from the mass detector area and the mass detector constant, derived from a suitable linear polyethylene homopolymer, or one of the polyethylene standards of known intrinsic viscosity (traceable to NBS 1475 homopolymer polyethylene reference sample).

The equation for IV(abs) is an area-based result using the baseline-subtracted specific-viscosity signal (DV) and the baseline-subtracted IR5 measurement sensor signal (applying the mass and viscosity constants), as determined from GPCOne™ software:

${I\; V_{({Abs})}} = {\frac{\sum\limits^{i}{DV}_{i}}{\sum\limits^{i}{IR}_{i}} \times {\left( {{Mass}\mspace{14mu}{Constant}\text{/}{Viscosity}\mspace{14mu}{constant}} \right).}}$ CDF Calculation Method for Each Chromatogram

The calculation of the following; a) cumulative detector fractions (CDF) from the IR5 measurement detector (“CDF_(IR)”), b) cumulative detector fractions from the low angle laser light scattering detector (“CDF_(LS)”), and c) cumulative detector fractions from the viscosity detector (“CDF_(DV)”), were each determined by the following steps (respectively, visually represented as FIG. 1, FIG. 2, and FIG. 3 for CDF_(IR) (IR 5 detector), CDF_(LS) (LS detector), and CDF_(DV) (viscosity detector)).

1) Linearly flow correct the chromatogram based on the relative retention volume ratio of the decane peak between the sample and that of a consistent MW narrow standards cocktail mixture.

2) Correct the light scattering detector offset relative to the IR 5 detector, as previously described. See above “Mourey and Balke” references.

3) Correct the viscosity detector offset relative to the IR 5 detector, as previously described. See above “Mourey and Balke” references.

4) Calculate the molecular weights at each “retention volume (RV) data slice” based on the polystyrene calibration curve, modified by the polystyrene to polyethylene conversion factor of approximately (0.43) as described previously, with a one point (slice) per second, and with a pump running at 1 ml/min.

5) Subtract baselines from each of the viscosity, light scattering, and infra-red chromatograms, and the integration window for each was set, making certain to integrate all of the low molecular weight retention volume range, where the low molecular weight retention volume range is observable (GPC profile greater than the baseline) from the infra-red chromatogram (thus setting the highest RV limit to the same index in each chromatogram). Material in the integration, which corresponds to a molecular weight less than 150 g/mol, is not included in any of the chromatograms.

6) Calculate the respective cumulative detector fraction (CDF) of the IR5 chromatogram (CDF_(IR)), LALLS chromatogram (CDF_(LS)), and viscosity chromatogram (CDF_(DV)), based on the baseline-subtracted peak height (H), from the high to low molecular weight (low to high retention volume), at each data slice (j), according to Equations 8A, 8B, or 8C, respectively:

$\begin{matrix} {{{CDF}_{IR} = \frac{\underset{{j = {{RV}\mspace{11mu}{of}\mspace{11mu} 10}},{000\mspace{11mu}{GPCMW}}}{\overset{j = {{RV}\mspace{11mu}{at}\mspace{11mu}{Highest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\sum H_{j}}}}{\underset{j = {{RV}\mspace{11mu}{or}\mspace{11mu}{Lowest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\overset{j = {{RV}\mspace{11mu}{at}\mspace{11mu}{Highest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\sum H_{j}}}}},} & \left( {{EQN}\mspace{14mu} 8A} \right) \\ {{{CDF}_{LS} = \frac{\underset{j = {{RV}\mspace{11mu}{of}\mspace{11mu}{Lowest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\overset{{j = {{RV}\mspace{11mu}{at}\mspace{11mu} 750}},{000\mspace{14mu}{GPCMW}}}{\sum H_{j}}}}{\underset{j = {{RV}\mspace{11mu}{at}\mspace{11mu}{Lowest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\overset{j = {{RV}\mspace{11mu}{at}\mspace{11mu}{Highest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\sum H_{j}}}}},} & \left( {{EQN}\mspace{14mu} 8B} \right) \\ {{CDF}_{DV} = {\frac{\underset{j = {{RV}\mspace{11mu}{at}\mspace{11mu}{Lowest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\overset{{j = {{RV}\mspace{11mu}{of}\mspace{11mu} 1}},2000,{000\mspace{14mu}{GPCMW}}}{\sum H_{j}}}}{\underset{j = {{RV}\mspace{11mu}{or}\mspace{11mu}{Lowest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\overset{j = {{RV}\mspace{11mu}{of}\mspace{11mu}{Highest}\mspace{11mu}{Integration}\mspace{11mu}{Volume}}}{\sum H_{j}}}}.}} & \left( {{EQN}\mspace{14mu} 8C} \right) \end{matrix}$

FIG. 1 depicts an example determination of the CDF_(IR) for Example 1: the fractional area of the IR5 measurement sensor channel of the detector (chromatogram) less than, or equal to, 10,000 g/mol MW, by GPC after baseline subtraction.

FIG. 2 depicts an example determination of the CDF_(LS) for Example 1: the fractional area of the 15 degree light scattering signal greater than, or equal to, 750,000 g/mol MW, by GPC after baseline subtraction.

FIG. 3 depicts an example determination of CDF_(DV) for Example 1: the fractional area of the specific viscosity signal greater than, or equal to, 1,200,000 g/mol MW, by GPC after baseline subtraction.

gpcBR Branching Index by Triple Detector GPC (TDGPC)

The gpcBR branching index was determined by first calibrating the light scattering, viscosity, and concentration detectors as described previously. Baselines were then subtracted from the light scattering, viscometer, and concentration chromatograms. Integration windows were then set, to ensure integration of all of the low molecular weight retention volume range in the light scattering and viscometer chromatograms that indicate the presence of detectable polymer from the refractive index chromatogram. Linear polyethylene standards were then used to establish polyethylene and polystyrene Mark-Houwink constants. Upon obtaining the constants, the two values were used to construct two linear reference conventional calibrations for polyethylene molecular weight and polyethylene intrinsic viscosity as a function of elution volume, as shown in Equations (9) and (10):

$\begin{matrix} {{M_{PE} = {\left( \frac{K_{PS}}{K_{PE}} \right)^{{1/\alpha_{PE}} + 1} \cdot M_{PS}^{\alpha_{PS} + {1/\alpha_{PE}} + 1}}},} & \left( {{EQN}\mspace{14mu} 9} \right) \\ {\lbrack\eta\rbrack_{PE} = {{K_{PS} \cdot M_{PS}^{\alpha + 1}}\text{/}{M_{PE}.}}} & \left( {{EQN}\mspace{14mu} 10} \right) \end{matrix}$

The gpcBR branching index is a robust method for the characterization of long chain branching as described in Yau, Wallace W., “Examples of Using 3D-GPC—TREF for Polyolefin Characterization,” Macromol. Symp., 2007, 257, 29-45. The index avoids the “slice-by-slice” 3D-GPC calculations traditionally used in the determination of g′ values and branching frequency calculations, in favor of whole polymer detector areas. From TDGPC data, one can obtain the sample bulk absolute weight average molecular weight (Mw, Abs) by the light scattering (LS) detector, using the peak area method. The method avoids the “slice-by-slice” ratio of light scattering detector signal over the concentration detector signal, as required in a traditional g′ determination.

With TDGPC, sample intrinsic viscosities were also obtained independently using Equations (11). The area calculation in this case offers more precision, because, as an overall sample area, it is much less sensitive to variation caused by detector noise and 3D-GPC settings on baseline and integration limits. More importantly, the peak area calculation was not affected by the detector volume offsets. Similarly, the high-precision, sample intrinsic viscosity (IV) was obtained by the area method shown in Equation (11):

$\begin{matrix} {{{I\; V} = {\lbrack\eta\rbrack = {{\sum\limits_{i}{w_{i}I\; V_{i}}} = {{\sum\limits_{i}{\left( \frac{C_{i}}{\sum\limits_{i}C_{i}} \right){IV}_{i}}} = {\frac{\sum\limits_{i}{C_{i}I\; V_{i}}}{\sum\limits_{i}C_{i}} = {\frac{\sum\limits_{i}{D\; P_{i}}}{\sum\limits_{i}C_{i}} = \frac{D\; P\mspace{14mu}{Area}}{{Conc}.\mspace{14mu}{Area}}}}}}}},} & \left( {{EQN}\mspace{14mu} 11} \right) \end{matrix}$ where DPi stands for the differential pressure signal monitored directly from the online viscometer. To determine the gpcBR branching index, the light scattering elution area for the sample polymer was used to determine the molecular weight of the sample. The viscosity detector elution area for the sample polymer was used to determine the intrinsic viscosity (IV or [η]) of the sample.

Initially, the molecular weight and intrinsic viscosity for a linear polyethylene standard sample, such as SRM1475a or an equivalent, were determined using the conventional calibrations (“cc”) for both molecular weight and intrinsic viscosity as a function of elution volume:

$\begin{matrix} {\lbrack\eta\rbrack_{cc} = {{\sum\limits_{i}{\left( \frac{C_{i}}{\sum\limits_{i}C_{i}} \right)I\; V_{i}}} = {\sum\limits_{i}{w_{i}I\;{V_{{cc},i}.}}}}} & \left( {{EQN}\mspace{14mu} 12} \right) \end{matrix}$

Equation (13) was used to determine the gpcBR branching index:

$\begin{matrix} {{{gpcBR} = \left\lbrack {{\left( \frac{\lbrack\eta\rbrack_{CC}}{\lbrack\eta\rbrack} \right) \cdot \left( \frac{M_{W}}{M_{W,{CC}}} \right)^{\alpha_{PE}}} - 1} \right\rbrack},} & \left( {{EQN}\mspace{14mu} 13} \right) \end{matrix}$ wherein [η] is the measured intrinsic viscosity, [η]_(cc) is the intrinsic viscosity from the conventional calibration (or cony GPC), Mw is the measured weight average molecular weight, and M_(w,cc) is the weight average molecular weight of the conventional calibration. The weight average molecular weight by light scattering (LS) is commonly referred to as “absolute weight average molecular weight” or “Mw(abs).” The M_(w,cc) from using conventional GPC molecular weight calibration curve (“conventional calibration”) is often referred to as “polymer chain backbone molecular weight,” “conventional weight average molecular weight” and “Mw(conv).”

All statistical values with the “cc or cony” subscript are determined using their respective elution volumes, the corresponding conventional calibration as previously described, and the concentration (Ci). The non-subscripted values are measured values based on the mass detector, LALLS, and viscometer areas. The value of KPE is adjusted iteratively, until the linear reference sample has a gpcBR measured value of zero. For example, the final values for a and Log K for the determination of gpcBR in this particular case are 0.725 and −3.355, respectively, for polyethylene, and 0.722 and −3.993, respectively, for polystyrene.

Once the K and a values have been determined using the procedure discussed previously, the procedure was repeated using the branched samples. The branched samples were analyzed using the final Mark-Houwink constants as the best “cc” calibration values.

The interpretation of gpcBR is straight forward. For linear polymers, gpcBR will be close to zero, since the values measured by LS and viscometry will be close to the conventional calibration standard. For branched polymers, gpcBR will be higher than zero, especially with high levels of long chain branching, because the measured polymer molecular weight will be higher than the calculated M_(w,cc), and the calculated IV_(cc) will be higher than the measured polymer IV. In fact, the gpcBR value represents the fractional IV change due to the molecular size contraction effect as a result of polymer branching. A gpcBR value of 0.5 or 2.0 would mean a molecular size contraction effect of IV at the level of 50% and 200%, respectively, versus a linear polymer molecule of equivalent weight.

For these particular examples, the advantage of using gpcBR, in comparison to a traditional “g′ index” and branching frequency calculations, is due to the higher precision of gpcBR. All of the parameters used in the gpcBR index determination are obtained with good precision, and are not detrimentally affected by the low TDGPC detector response at high molecular weight from the concentration detector. Errors in detector volume alignment also do not affect the precision of the gpcBR index determination.

Calculation of LCB Frequency

The LCB_(f) was calculated for each polymer sample by the following procedure:

1) The light scattering, viscosity, and concentration detectors with a calibration traceable to NIST-NBS 1475 homopolymer polyethylene (or equivalent reference).

2) The light scattering and viscometer detector offsets were corrected relative to the concentration detector as described above in the calibration section (see references to Mourey and Balke).

3) Baselines were subtracted from the light scattering, viscometer, and concentration chromatograms and set integration windows making certain to integrate all of the low molecular weight retention volume range in the light scattering chromatogram that is observable from the refractometer chromatogram. 4) A linear homopolymer polyethylene Mark-Houwink reference line was established by injecting a standard with a polydispersity of at least 3; the data file was calculated (from above calibration method), and the intrinsic viscosity and molecular weight were determined using the mass constant corrected data for each chromatographic slice. 5) The LDPE sample of interest was analyzed, the data file (from above calibration method) was calculated, and the intrinsic viscosity and molecular weight from the mass constant, corrected data for each chromatographic slice, were recorded. At lower molecular weights, the intrinsic viscosity and the molecular weight data may need to be extrapolated such that the measured molecular weight and intrinsic viscosity asymptotically approach a linear homopolymer GPC calibration curve. 6) The Mark-Houwink plot of the linear homopolymer polyethylene standard reference with MWD of 3 or greater (e.g., polyethylene homopolymer, Mn=43,000 g/mol, Mw=120,000 g/mol, MWD=2.79; no long chain branching) was shifted as follows: the intrinsic viscosity was shifted at each point (i) by the following factor: IVi=IVi*0.964 where IV is the intrinsic viscosity. 7) The Mark-Houwink plot of the linear homopolymer polyethylene standard reference with PDI of 3, or greater, was shifted as follows: the molecular weight (M) was shifted at each point (i) by the following factor: Mi=Mi*1.037, where M is the molecular weight. 8) The g′ at each chromatographic slice was calculated as follows: g′=(IV(LDPE)/IV(linear reference)), at the same M. The IV(linear reference) was calculated from a fifth-order polynomial fit of the reference Mark-Houwink Plot and where IV(linear reference) is the intrinsic viscosity of the linear homopolymer polyethylene reference (adding an amount of SCB (short chain branching) to account for backbiting through 6) and 7) at the same molecular weight (M)). The IV ratio is assumed to be one at molecular weights less than 3,500 g/mol to account for natural scatter in the light scattering data. 9) The number of branches at each data slice was calculated as follows:

$\left\lbrack \frac{I\; V_{LDPE}}{I\; V_{linear\_ reference}} \right\rbrack_{M}^{1.33} = {\left\lbrack {\left( {1 + \frac{B_{n}}{7}} \right)^{1/2} + {\frac{4}{9}\frac{B_{n}}{\pi}}} \right\rbrack^{{- 1}/2}.}$ 10) The average LCB quantity was calculated across all of the slices (i), as follows:

${LCB}_{1000C} = {\frac{\sum\limits_{M = 3500}^{i}\left( {\frac{B_{ni}}{14000}c_{i}} \right)}{\sum c_{i}}.}$ Differential Scanning Calorimetry (DSC)

Differential Scanning Calorimetry (DSC) can be used to measure the melting and crystallization behavior of a polymer over a wide range of temperatures. For example, the TA Instruments Q2000 DSC, equipped with an RCS (refrigerated cooling system) and an autosampler is used to perform this analysis. During testing, a nitrogen purge gas flow of 50 ml/min is used. Each sample is melt pressed into a thin film at about 190° C.; the melted sample is then air-cooled to room temperature (˜25° C.). The film sample was formed by pressing a “0.5 to 0.9 gram” sample at 190° C. at 20,000 lb_(f) and 10 seconds, to form a “0.1 to 0.2 mil thick” film. A 3-10 mg, six mm diameter specimen was extracted from the cooled polymer, weighed, placed in an aluminum pan (about 50 mg), and crimped shut. Analysis was then performed to determine its thermal properties.

The thermal behavior of the sample was determined by ramping the sample temperature up and down to create a heat flow versus temperature profile. First, the sample was rapidly heated to 180° C., and held isothermal for five minutes, in order to remove its thermal history. Next, the sample was cooled to −40° C., at a 10° C./minute cooling rate, and held isothermal at −40° C. for five minutes. The sample was then heated to 150° C. (this is the “second heat” ramp) at a 10° C./minute heating rate. The cooling and second heating curves are recorded. The cooling curve was analyzed by setting baseline endpoints from the beginning of crystallization to −20° C. The heating curve was analyzed by setting baseline endpoints from −20° C. to the end of melting. The values determined were peak melting temperature (Tm), peak crystallization temperature (Tc), heat of fusion (Hf) (in Joules per gram), and the calculated % crystallinity for ethylene-based polymer samples using the following equations: % Crystallinity=((Hf)/(292 J/g))×100 (EQN 14). The heat of fusion and the peak melting temperature are reported from the second heat curve. The peak crystallization temperature is determined from the cooling curve.

Film Testing

The following physical properties were measured on the films as described in the experimental section. Prior to testing, the film was conditioned for at least 40 hours (after film production) at 23° C. (+/−2° C.) and 50% relative humidity (+/−5% R.H). See Tables 13-16 for the thickness of each film.

Total (Overall) Haze and Internal Haze: Internal haze and total haze were measured according to ASTM D 1003-07. Internal haze was obtained via refractive index matching using mineral oil (1-2 teaspoons), which was applied as a coating on each surface of the film. A Hazegard Plus (BYK-Gardner USA; Columbia, Md.) was used for testing. For each test, five samples were examined, and an average reported. Sample dimensions were “6 in×6 in”. 45° Gloss: ASTM D2457-08 (average of five film samples; each sample “10 in×10 in”), Clarity: ASTM D1746-09 (average of five film samples; each sample “10 in×10 in”); 2% Secant Modulus—MD (machine direction) and CD (cross direction): ASTM D882-10 (average of five film samples in each direction). 1 inch wide test strips are loaded in a tensile testing frame using line contact grips at a contact point (gauge length) separation of 4 inches. Samples are tested at a crosshead speed of 2 inches/min up to a nominal stain of 5%.

MD and CD Elmendorf Tear Strength: ASTM D1922-09. The force in grams required to propagate tearing across a film or sheeting specimen is measured using a precisely calibrated pendulum device. Acting by gravity, the pendulum swings through an arc, tearing the specimen from a precut slit. The specimen is held on one side by the pendulum and on the other side by a stationary member. The loss in energy by the pendulum is indicated by a pointer or by an electronic scale. The scale indication is a function of the force required to tear the specimen. The sample used is the ‘constant radius geometry’ as specified in D1922. Testing would be typically carried out on samples that have been cut from both the MD and CD directions. Prior to testing, the sample thickness is measured at the sample center. A total of 15 specimens per direction are tested, and the average tear strength is reported. Samples that tear at an angle greater than 60° from the vertical are described as ‘oblique’ tears—such tears should be noted, though the strength values are included in the average strength calculation.

Dart: ASTM D1709-09. The test result is reported by Method A, which uses a 1.5″ diameter dart head and 26″ drop height. The sample thickness is measured at the sample center, and the sample is then clamped by an annular specimen holder with an inside diameter of 5 inches. The dart is loaded above the center of the sample and released by either a pneumatic or electromagnetic mechanism. Testing is carried out according to the ‘staircase’ method. If the sample fails, a new sample is tested with the weight of the dart reduced by a known and fixed amount. If the sample does not fail, a new sample is tested with the weight of the dart increased by a known increment. After 20 specimens have been tested the number of failures is determined. If this number is 10 then the test is complete. If the number is less than 10, the testing continues until 10 failures have been recorded. If the number is greater than 10, testing is continued until the total number of non-failures is 10. The dart (strength) is determined from these data as per ASTM D1709.

Puncture Strength: Puncture was measured on an INSTRON Model 4201 with SINTECH TESTWORKS SOFTWARE Version 3.10. The specimen size was “6 in×6 in,” and five measurements were made to determine an average puncture value. A “100 lb load cell” was used with a round specimen holder of 4 inch diameter. The puncture probe was a ½ inch diameter, polished, stainless steel ball on a 0.25 inch diameter support rod with a 7.5 inch maximum travel length.′ There was no gauge length, and prior to the start of the test, the probe was as close as possible to, but not touching, the specimen. The puncture probe was pushed into the center of the clamped film at a cross head speed of 10 inches/minute. A single thickness measurement was made in the center of the specimen. For each specimen, the puncture (ft·lb_(f) per in³) was determined. The puncture probe was cleaned using a “KIM-WIPE” after each specimen.

Experimental

Preparation of Inventive Ethylene-Based Polymers

FIG. 4 is a block diagram of the process reaction system used to produce the inventive ethylene-based polymers (LDPEs). The process reaction system in FIG. 4 is a partially closed-loop, dual recycle, high-pressure, low density polyethylene production system. The process reaction system is comprised of a fresh ethylene feed line [1], a booster compressor (“Booster”), a primary compressor (“Primary”), a hypercompressor (“Hyper”) and a four zone tubular reactor (“4 Zone Reactor”). Stream [3] is heated by a “Pre-heater” to a sufficiently high temperature, and fed to the front of the reactor. Stream [11] is fed as a side stream to the reactor. In the reactor, polymerization is initiated with the help of four mixtures, each containing one or more free radical initiation systems (see Table 1), which are injected at the inlet of each reaction zone (not shown).

The maximum temperature in each reaction zone is controlled at a set point, by regulating the feed amount of the mixture of initiators at the start of each reaction zone. Each reaction zone has one inlet and one outlet. Each inlet stream consists of the outlet stream from the previous zone and/or added ethylene-rich feed stream. Upon completing the polymerization, the reaction mixture is depressurized and cooled in stream [4]. The process further consists of a high pressure separator “HPS,” which separates the reaction mixture into an ethylene rich stream [8], which is cooled, and recycled back to the suction of the hyper, and a polymer rich stream [5], which is sent to the low pressure separator “LPS” for further separation. In the LPS, the ethylene rich stream is cooled, and recycled back to the booster (“Booster”) in stream [6]. From the booster, the ethylene is then compressed further by the primary compressor. The feed [2] is sent to the suction of the hypercompressor. The polymer leaving the LPS [7] is further pelletized and purged. The chain transfer agent “CTA” feed [10] is injected into the ethylene stream at the discharge of the primary compressor. Stream [9] is a purge stream used to remove impurities and/or inerts. Cooling jackets (using high pressure water) are mounted around the outer shell of the tube reactor and pre-heater.

For Inventive Examples 1-2, a mixture containing t-butyl peroxy-2 ethylhexanoate (TBPO), tert-butyl peroxyacetate (TBPA), and an iso-paraffinic hydrocarbon solvent (boiling range 171-191° C.; for example, ISOPAR H) was used as the initiator mixture for the first reaction zone. For the second reaction zone, a mixture containing di-tert-butyl peroxide (DTBP), TBPO, TBPA, and the iso-paraffinic hydrocarbon solvent was used. For the third and fourth reaction zones, a mixture of TBPA, DTBP, and iso-paraffinic hydrocarbon solvent was used. This data is summarized in Table 1. Propylene was used as the CTA. The concentration of the CTA fed to the process was adjusted to control the melt index of the product. Table 2 shows that the polymerization conditions used to form the inventive samples were relatively low reactor pressures and high reactor peak temperatures, in order to maximize the molecular weight distribution of the polymer. The molecular weight of each polymer was also maximized by reducing the CTA (propylene) concentration fed to the reactor. It was discovered that these polymerization conditions produced a “LDPE resin” with a broad molecular weight distribution (MWD).

TABLE 1 Peroxide initiator flows, in pounds per hour, at each injection point Injection Example 1 (0.5 MI) Example 2 (1.3 MI) Point Initiator Neat PO lbs/hour Neat PO lbs/hour #1 TBPO 3.4 3.4 #1 TBPA 1.5 1.5 #2 TBPO 9.4 10.4 #2 TBPA 2.7 3.0 #2 DTBP 1.3 1.5 #3 TBPA 0.92 0.92 #3 DTBP 2.2 2.2 #4 TBPA 0.52 0.76 #4 DTBP 1.2 1.8

TABLE 2 Process conditions used to polymerize Examples Process Variables Ex 1 (0.5 MI) Ex. 2 (1.3 MI) Reactor Pressure (Psig) 31,545 31,500 Zone 1 Initiation T (° C.) 143 143 Zone 1 Peak T (° C.) 277 272 Zone 2 Initiation T (° C.) 155 157 Zone 2 Peak T (° C.) 303 303 Zone 3 Initiation T (° C.) 255 250 Zone 3 Peak T (° C.) 296 294 Zone 4 Initiation T (° C.) 265 258 Zone 4 Peak T (° C.) 295 295 Fresh ethylene Flow (lb/hr) 26,100 26,300 Ethylene Throughput to Reactor (lb/hr) 101,340 100,910 Ethylene Conversion (%) 25.8 26.1 Propylene Flow (lb/hr) 75 150 Ethylene Purge Flow (lb/hr) 497 495 Recycle Prop Conc. (% Vol) 0.24 0.47 Pre-heater T (° C.) 200 200 Reactor Cooling System 1 (° C.) 188 188 Reactor Cooling System 2 (° C.) 185 185

Properties of Inventive Examples and Comparative Examples are listed in Tables 3-11. Table 3 contains the melt index (I2 or MI), density, % hexane extractables, and melt strength data. A comparable melt indexes, the Inventive Examples exhibit a good and relatively high melt strength, and provide a good balance of bubble stability, in combination with high output on blown film lines, and good mechanical properties, as compared to the comparative examples at similar melt index. FIG. 5 is a plot of the melt strength versus the melt index for the samples of Table 3, and this figure shows that these inventive polymers (Ex. 1 and Ex. 2) have a melt strength, at 190° C., greater than “−2.5*(I₂ at 190° C.)+15.5 cN”, and less than “−2.5*(I₂ at 190° C.)+20.5 cN”. The melt indexes for inventive examples, as shown in Table 3, are comparable to that of the comparative examples; however, the melt strength of each inventive example is higher than that of the respective comparative example, at similar melt index and density.

TABLE 3 Density, melt index (I₂), % hexane extractables, and peak melt strength (MS) at 190° C. of Inventive Examples (IE) and Comparative Examples (CE). Density I₂ Hexane Melt Ex. (g/cc) (g/10 min) Extractables (%) Strength (cN) IE-1 0.9203 0.51 2.13 18.3 IE-2 0.9197 1.34 2.29 13.5 CE-1^(a) 0.9200 1.82 2.35 9.0 CE-2^(b) 0.9176 0.43 1.80 26.6 CE-3^(c) 0.9172 1.5 NM 19.2 CE-4^(d) 0.9231 2.0 NM 8.4 CE-5^(e) 0.9191 2.0  NM. 7.7 ^(a)AGILITY 1021 available from the Dow Chemical Company. ^(b)LDPE 662I available from the Dow Chemical Company ^(c)See example IE2 from W02014/190036 ^(d)LDPE 640I available from the Dow Chemical Company ^(e)LDPE 450E available from the Dow Chemical Company. NM = not measured.

Tables 4 through Table 6 contain the TDGPC data, illustrating for the inventive polymers the relatively broad, and optimized, molecular weight distribution or Mw(conv)/Mn(conv) ratio, and the relatively high z-average molecular weight, Mz(conv), and high weight average molecular weight, Mw(conv), all of which contribute to the higher melt strength and good output on blown film lines, as seen with these inventive polymers.

Table 5 contains the TDGPC-related properties derived from the LS and viscosity detectors, in conjunction with the concentration detector. As seen in Table 5, it has been discovered that the inventive polymers have a relatively high, and optimized, Mw(abs), Mz(abs), and Mw(abs)/Mw(conv). These higher values correlate with relatively high melt strength and good output, as seen on blown film lines, using the inventive polymers. It has been discovered that the inventive polymers have a high amount of long branching (LCBf and/or gpcBR), at a relatively high Mw (Mw(abs)), and substantial ultra-high MW material (Mz(abs)), all of which contribute to the desired melt strength and improved processability (for example, increased blown film output and decreased screen pressure). As mentioned, the melt strength is similar, or higher, for the Inventive Examples as compared to the respective comparative examples, and this is primarily due to the design of the inventive polymers as described by the TDGPC molecular weight features. The design of the inventive polymers is to provide higher melt index polymers that have an optimum melt strength, and a good balance of physical properties, along with good drawability, bubble stability, and blown film output, when forming films, with or without an additional polymer, such as a LLDPE.

Table 6 contains several unique TDGPC properties, which further reflect the differences in structure between the Inventive Examples and Comparative Examples. The CDF_(IR), CDF_(LS), and CDF_(DV) determinations are from the fractional baseline-subtracted chromatographic areas, versus the whole chromatogram, using the limits as expressed in Equations 8A, 8B, and 8C above. The Mw(abs) is determined from the mass-normalized area of the baseline-subtracted “15 degree light scattering signal,” and the IV(Abs) is determined from the mass-normalized area of the baseline-subtracted specific viscosity chromatogram. The Mw(abs) is compared (ratio taken) against the conventional weight-average molecular weight (Mw(conv)), and this ratio is an indication of the “total molecular weight (including all branching)” to the “backbone molecular weight of the polymer.” It has been discovered that these polymers contain high levels of long chain branches without a significant increase in overall molecular weight. In addition, the ethylene-based polymers have a significant amount of low molecular weight polymer for improved processability. These features are represented by the equation “(Mw(abs)/Mw(conv)−2.00)*(100,000 g/mol/Mw(abs))*CDF_(IR) (MW≤10,000 g/mol)≥0.030.”

Table 8 contains the DMS viscosity data, as summarized by the viscosities measured at 0.1, 1, 10, and 100 rad/s, the viscosity ratio, or the ratio of viscosity measured at 0.1 rad/s to the viscosity measured at 100 rad/s, all being measured at 190° C., and the tan delta measured at 0.1 rad/s and 190° C. The viscosity ratio, which reflects the change in viscosity with frequency, is, like the low frequency viscosity, relatively high for the inventive polymers, as compared to the respective comparative polymers. The high ratio values are reflective of the good processability of the Inventive Examples when making blown film. The tan delta, at 0.1 rad/s, values of the inventive polymers are relatively low, indicative of high melt elasticity, which may also be correlated with good blown film bubble stability.

Table 9 contains the branches per 1000 total carbons as measured by ¹³C NMR. These LDPE polymers contain amyl, or C5 branches, which are not contained in substantially linear polyethylenes, such as AFFINITY Polyolefin Plastomers, or the LLDPEs, such as DOWLEX Polyethylene Resins, both produced by The Dow Chemical Company. Each inventive and comparative LDPE, shown in Table 9, contains greater than, or equal to, 0.5 amyl groups (branches) per 1000 total carbon atoms (the Inventive Examples contain greater than 1 amyl groups (branches) per 1000 total carbon atoms). The Inventive Examples contain relatively low levels of C1 per 1000 total carbon atoms, in which C1 is attributable to the propylene used as a CTA. The respective Comparative Examples contain higher levels of C1 per 1000 total carbon atoms. The Inventive Examples are also shown to contain higher levels of 1,3-diethyl branches per 1000 total carbon atoms, higher levels of C2 on the quaternary carbon per 1000 total carbon atoms, higher levels of C4 per 1000 total carbon atoms, and high levels of C5 (amyl group) per 1000 total carbon atoms. Table 10 contains unsaturation results by ¹H NMR. Table 11 contains the DSC results of the melting point, T_(m), the heat of fusion, the percent crystallinity, and the crystallization point, T_(c).

TABLE 4 Conventional GPC properties of Examples (Ex.) and Comparative Examples (CE). Mn(conv) Mw(conv) Mz(conv) Ex. (g/mol) (g/mol) (g/mol) Mw(conv)/Mn(conv) IE-1 15,600 142,900 591,400 9.15 IE-2 13,500 115,800 522,300 8.60 CE-1 13,700 100,800 421,000 7.34 CE-2 22,900 233,700 801,000 10.22 CE-3 12,400 128,200 412,600 10.35 CE-4 18,100 87,000 244,000 4.80 CE-5 15,600 88,700 254,700 5.69

TABLE 5 Absolute GPC calibration of Examples (Ex.) and Comparative Examples (CE). Mw (abs) Mz (abs) Mz (abs)/ Mw (abs)/ Ex. (g/mol) (g/mol) Mw (abs) Mw (conv) LCBf gpcBR IE-1 397,000 4,990,000 12.59 2.78 3.28 2.98 IE-2 304,000 4,600,000 15.11 2.63 3.26 2.67 CE-1 243,000 4,830,000 19.91 2.41 2.60 2.24 CE-2 854,000 4,730,000 5.55 3.65 3.66 4.89 CE-3 242,000 1,058,000 4.37 1.89 3.88 1.49 CE-4 158,000 948,000 5.99 1.82 3.55 1.52 CE-5 156,000 1,010,000 6.46 1.76 4.83 1.99

TABLE 6 TDGPC-related properties related to IR, LS, and DV of Examples (Ex.) and Comparative Examples (CE). CDF_(IR) CDF_(LS) CDF_(DV) IV (MW ≤ 10,000 (MW ≥ 750,000 (MW ≥ 1,200,000 (Abs) Ex. g/mol) g/mol) g/mol) (g/dl) IE-1 0.154 0.517 0.044 1.065 IE-2 0.176 0.450 0.029 0.949 CE-1^(a) 0.174 0.426 0.018 0.919 CE-2 0.109 0.620 0.107 1.249 CE-3 0.185 0.190 0.010 1.001 CE-4 0.134 0.127 0.002 0.911 CE-5 0.149 0.124 0.002 0.906

TABLE 7 Relationship between Mw(abs), Mw(conv), and CDF_(IR) (MW below 10,000 g/mol) for inventive and comparative examples. (Mw(abs)/Mw(conv) − 2.00)*(100,000 Ex. g/mol/Mw(abs))*CDF_(IR) (MW < 10,000 g/mol) IE-1 0.033 IE-2 0.036 CE-1 0.029 CE-2 0.018 CE-3 −0.0043 CE-4 −0.0069 CE-5 −0.010

TABLE 8 Viscosities in Pa · s at 0.1, 1, 10, and 100 rad/s, the viscosity ratio, and the tan delta at 190° C. Visc Visc 1 Visc Visc Visc. Ratio Tan Delta Ex. 0.1 rad/s rad/s 10 rad/s 100 rad/s V0.1/V100 0.1 rad/s IE-1 22,883 8,772 2,559 629 36.38 1.62 IE-2 11,001 5,208 1,781 490 22.43 2.47 CE-1 9,005 4,622 1,652 462 19.48 3.01 CE-2 19,317 7,610 2,388 626 30.84 1.69 CE-3 10,807 4,685 1,508 404 26.74 3.99 CE-4 5,853 3,945 1,721 535 10.93 6.09 CE-5 7,442 4,288 1,654 488 15.24 2.06

TABLE 9 ¹³C NMR Branching results in branches per 1000 C: Examples and Comp. Examples. C2 on Quat Ex. C1 1,3 diethyl branches Carbon C4 C5 C6+ IE-1 0.66 4.39 1.50 6.78 2.43 3.4 IE-2 1.30 4.42 1.59 6.68 2.25 3.4 CE-1^(a) 2.11 4.09 1.41 6.54 2.22 3.4 CE-2 ND 4.58 1.82 7.08 2.23 3.1 CE-3 ND 5.35 2.02 7.50 2.23 4.3 CE-4 ND 4.77 1.90 6.58 2.21 3.5 CE-5 ND 3.37 1.37 7.09 1.88 3.2 ND = Not detected.

TABLE 10 Unsaturation results by ¹H NMR of Examples and Comp. Examples. total Vi- cis and trisub/ vinylidene/ unsat- Ex. nyl/1000C trans/1000C 1000C 1000C uration/1000C IE-1 0.128 0.051 0.08 0.204 0.46 IE-2 0.120 0.046 0.068 0.200 0.43 CE-1 0.162 0.048 0.057 0.176 0.44 CE-2 0.042 0.129 0.072 0.245 0.49 CE-3 0.073 0.059 0.141 0.310 0.58 CE-4 0.057 0.054 0.117 0.282 0.51 CE-5 0.038 0.026 0.063 0.150 0.28

TABLE 11 DSC results of Examples and Comp. Examples. Ex. Tm (° C.) Heat of Fusion (J/g) % Crystallinity Tc (° C.) IE-1 109.4 139.1 47.6 97.8 IE-2 109.0 139.6 47.8 97.0 CE-1^(a) 108.1 136.5 46.7 96.1 CE-2^(b) 107.9 137.8 47.2 96.2 CE-3^(c) 108.1 144.7 49.6 95.7 CE-4^(d) 110.2 145.0 49.7 96.6 CE-5^(e) 111.7 151.5 51.9 99.5 Film Formulations and Production of Blown Films

Blown films were made, and properties measured, with different LDPEs and one LLDPE1 (DOWLEX 2045G). LLDPE1 had a “1.0 melt index (MI or I2), and a 0.920 g/cc density.” Films were made at 10 wt % and 20 wt % of the respective LDPE, based on the weight of the LDPE and LLDPEL Each formulation was compounded on a MAGUIRE gravimetric blender. A polymer processing aid (PPA), DYNAMAR FX-5920A, was added to each formulation. The PPA was added at “1.125 wt % of masterbatch,” based on the total weight of the formulation. The PPA masterbatch (Ingenia AC-01-01, available from Ingenia Polymers) contained 8 wt % of DYNAMAR FX-5920A in a polyethylene carrier. This amounts to 900 ppm PPA in the polymer. LLDPE1 was also used in the films made at maximum output. Samples were run at maximum output with 80 wt % LLDPE1 and 20 wt % LDPE, and 90 wt % LLDPE1 and 10 wt % LDPE. The monolayer blown films were made on an “8 inch die” with a polyethylene “Davis Standard Barrier II screw.” External cooling by an air ring and internal bubble cooling were used. General blown film parameters, used to produce each blown film, are shown in Table 12. The temperatures are those closest to the pellet hopper (Barrel 1), and in increasing order, as the polymer was extruded through the die.

TABLE 12 Blown film fabrication conditions for films. Condition A Condition B Blow up ratio (BUR) 2.5 2.5 Film thickness (mil) 2.0 1.0 Die gap (mil) 70 70 Air temperature (° F.) 45 45 Temperature profile (° F.) Barrel 1 350 350 Barrel 2 415 415 Barrel 3 365 365 Barrel 4 305 305 Barrel 5 305 305 Screen Temperature 410 410 Adapter 410 410 Block 430 430 Lower Die 440 440 Inner Die 440 440 Upper Die 440 440 Production of Films for Determination of Maximum Output Rate of Blown Film

Film samples were made at a controlled rate and at a maximum rate. The controlled rate was 250 lb/hr, which equals an output rate of 10.0 lb/hr/inch of die circumference. The die diameter used for the maximum output trials was an 8 inch die, so that for the controlled rate, as an example, the conversion between “lb/hr” and “lb/hr/inch” of die circumference, is shown in Equation 15. Similarly, such an equation can be used for other rates, such as the maximum rate, by substituting the maximum rate in Eqn. 15 to determine the “lb/hr/inch” of die circumf. Lb/Hr/Inch of Die Circumference=(250 Lb/Hr)/(8*π)=10  (Eqn. 15).

The maximum rate for a given sample was determined by increasing the output rate to the point where bubble stability was the limiting factor. The extruder profile was maintained for both samples (standard rate and maximum rate), however the melt temperature was higher for the maximum rate samples, due to the increased shear rate with higher motor speed (rpm, revolutions per minute). The maximum bubble stability was determined by taking the bubble to the point where it would not stay seated in the air ring. At that point, the rate was reduced to where the bubble was reseated in the air ring, and then a sample was collected. The cooling on the bubble was adjusted by adjusting the air ring and maintaining the bubble. This was taken as the maximum output rate, while maintaining bubble stability. Film properties are listed in Tables 13-16.

TABLE 13 Film Properties* of “100% LLDPE1;” and “90 wt % LLDPE1/10 wt % LDPE” films. Film 1 2 3 4 5 LDPE NA CE 2 IE-1 NA IE-1 Thickness (mil) 1.97 1.98 2.06 0.991 0.982 Melt Index I₂ 1.01 N.D. 0.873 0.99 0.867 Melt Index Ratio I₁₀/I₂ 7.76 N.D. 8.44 7.83 8.55 Density (g/cc) 0.922 N.D. 0.923 0.922 0.922 Haze (%) 11.1 13.1 9.16 11.5 6.59 Haze Internal (%) 4.6 4.4 3.84 2.12 1.31 Gloss (45°) 55.8 53.3 64.34 49.14 63.82 Clarity (%) 98.6 93.0 98.6 97.9 97.8 Dart (g) 412 259 265 233 148 Puncture (ft-lb_(f)/in³) 183 245 218 243 224 MD Tear (g) 842 588 614 303 188 CD Tear (g) 1,092 1,045 1,280 289 665 MD Normalized Tear (g/mil) 442 298 298 604 180 CD Normalized Tear (g/mil) 561 524 609 577 621 2% MD Secant Modulus (psi) 27,300 30,100 30,700 32,000 35,800 2% CD Secant Modulus (psi) 32,400 36,200 35,100 37,300 41,000 Frost Line Height (inches) 30 35 31 34 32 Melt Temperature (° F.) 409 439 407 411 407 Screen Pressure (psi) 3,610 3740 3820 3850 3770 Standard output (lb/hr) 248 252 252 249 249 Frost Line Height (inches), Max Output 52 80 N.D. N.D. 77 Melt Temperature (° F.), Max Output 422 460 N.D. 421 430 Screen Pressure (psi), Max Output 3,980 4450 N.D. 4390 4650 Output (lb/hr), Max Output 319 403 N.D. 330 391 *Film properties with relevant comparative to IE-1, each made at either 2 mil (Condition A) or 1 mil (Condition B) at a standard rate of 250 lb/hr. Note, the melt temperature, screen pressure and output were each measured at a maximum rate. N.D. = not determined.

TABLE 14 Film properties* of “100% LLDPE1;” and “90 wt % LLDPE1/10 wt % LDPE” films. Film 1 6 7 8 9 10 4 11 12 LDPE NA CE-1 CE-3 CE-4 CE-5 IE-2 NA CE-1 IE-2 Thickness (mil) 1.97 1.89 1.93 1.82 1.88 2.05 0.991 1.01 0.896 Melt Index I₂ 1.01 N.D. N.D. N.D. N.D. .909 0.99 0.933 0.909 Melt Index Ratio I₁₀/I₂ 7.76 N.D. N.D. N.D. N.D. 8.57 7.83 8.22 8.62 Density (g/cc) 0.922 N.D. N.D. N.D. N.D. 0.923 0.922 0.922 0.923 Haze (%) 11.1 8.4 8.4 9.5 9.4 9.73 11.5 6.25 5.6 Haze Internal (%) 4.6 4.1 3.7 4.6 4.4 4.14 2.12 1.52 1.33 Gloss (45°) 55.8 69.1 67.6 66.5 66.2 63.64 49.14 67.06 66.7 Clarity (%) 98.6 99.4 98.2 99.0 99.3 98.7 97.9 99.0 98.5 Dart (g) 412 295 292 289 304 280 233 157 140 Puncture (ft-lb_(f)/in³) 183 236 256 253 230 172 243 232 220 MD Tear (g) 842 675 599 690 772 613 303 194 200 CD Tear (g) 1,092 1,244 1,074 1,188 1,300 1275 289 700 637 MD Normalized Tear (g/mil) 442 342 310 360 374 293 604 189 199 CD Normalized Tear (g/mil) 561 646 559 644 641 606 577 668 637 2% MD Secant Modulus (psi) 27,300 31,300 33,600 31,200 32,700 29,900 31,600 34,000 33,000 2% CD Secant Modulus (psi) 32,400 35,400 36,000 34,700 34,500 34,200 37,300 40,800 41,100 Frost Line Height (inches) 30 38 38 38 38 32 34 31 32 Melt Temperature (° F.) 409 442 442 443 444 406 411 406 407 Screen Pressure (psi) 3,610 3290 3420 3330 3410 3830 3850 3890 3760 Standard output (lb/hr) 248 250 251 249 254 250 249 250 254 Frost Line Height (in), Max 52 75 82 72 72 N.D. N.D. 67 69 Output Melt Temp. (° F.), Max 422 461 464 461 461 N.D. 421 425 428 Output Screen Pressure (psi), Max 3,980 4160 4250 4010 3900 N.D. 4390 4450 4450 Output Output (lb/hr), Max Output 319 402 426 383 377 N.D. 330 369 398 *Film properties with relevant comparative to IE-2, each made at either 1 mil or 2 mil at a standard rate of 250 lb/hr. Note, the melt temperature, screen pressure and output were each measured at a maximum rate. N.D. = not determined.

TABLE 15 Film properties of “100% LLDPE1;” and “80 wt % LLDPE1/20 wt % LDPE” films. Film 1 13 14 4 15 LDPE NA CE-2 IE-1 NA IE-1 Thickness (mil) 1.97 1.96 1.97 0.991 0.966 Melt Index I₂ 1.01 N.D. 0.776 0.99 0.752 Melt Index Ratio I₁₀/I₂ 7.76 N.D. 8.88 7.83 9.09 Density (g/cc) 0.922 N.D. 0.922 0.922 0.922 Haze (%) 11.1 15.3 8.82 11.5 6.71 Haze Internal (%) 4.6 2.7 2.75 2.12 1.00 Gloss (45°) 55.8 44.4 60.5 49.14 61.72 Clarity (%) 98.6 82.3 95.7 97.9 95.4 Dart (g) 412 244 259 233 139 Puncture (ft-lb_(f)/in³) 183 209 179 243 195 MD Tear (g) 842 408 412 303 103 CD Tear (g) 1,092 1,006 1283 289 654 MD Normalized Tear (g/mil) 442 208 197 604 103 CD Normalized Tear (g/mil) 561 509 598 577 629 2% MD Secant Modulus (psi) 27,300 29,700 29,200 32,000 35,800 2% CD Secant Modulus (psi) 32,400 37,200 34,200 37,300 44,400 Frost Line Height (inches) 30 35 27 34 30 Melt Temp. (° F.) 409 441 405 411 405 Screen Pressure (psi) 3,610 3,730 3930 3850 3910 Standard Output (lb/hr) 248 251 250 249 253 Frost Line Height (inches), Max Output 52 85 N.D. N.D. 79 Melt Temperature (° F.), Max Output 422 482 N.D. 421 438 Screen Pressure (psi), Max Output 3,980 5200 N.D. 4390 4670 Output (lb/hr), Max Output 319 577 N.D. 330 449 *Film properties relevant comparative to IE-1, each made at either 1 mil or 2 mil at a standard rate of 250 lb/hr. Note, the melt temperature, screen pressure and output were each measured at a maximum rate. N.D. = not determined.

TABLE 16 Film properties of “100% LLDPE1;” and “80 wt % LLDPE1/20 wt % LDPE” Films Film 1 16 17 18 19 20 4 21 22 LDPE NA CE-1 CE-3 CE-4 CE-5 IE-2 NA CE-1 IE-2 Thickness (mil) 1.97 1.90 1.99 1.91 1.93 1.99 0.991 1.02 0.933 Melt Index I₂ 1.01 N.D. N.D. N.D. N.D. 0.838 0.99 0.89 0.860 Melt Index Ratio I₁₀/I₂ 7.76 N.D. N.D. N.D. N.D. 9.13 7.83 8.92 8.99 Density (g/cc) 0.922 N.D. N.D. N.D. N.D. 0.922 0.922 0.923 0.922 Haze (%) 11.1 7.5 8.3 7.8 7.0 7.78 11.5 4.41 4.87 Haze Internal (%) 4.6 4.3 3.5 4.6 4.0 3.37 2.12 2.29 1.03 Gloss (45°) 55.8 75.1 67.4 75.2 78.0 67.04 49.14 76.00 69.46 Clarity (%) 98.6 99.2 95.2 99.2 99.2 98.4 97.9 98.7 97.3 Dart (g) 412 235 220 253 217 248 233 133 127 Puncture (ft-lb_(f)/in³) 183 200 205 218 209 175 243 192 189 MD Tear (g) 842 462 426 465 453 444 303 124 129 CD Tear (g) 1,092 1,209 1,149 1,251 1,339 1305 289 708 658 MD Normalized Tear 442 236 213 236 229 218 604 126 129 (g/mil) CD Normalized Tear 561 603 566 631 691 635 577 676 634 (g/mil) 2% MD Secant 27,300 29,100 27,400 27,900 28,900 29,100 32,000 34,100 33,800 Modulus (psi) 2% CD Secant 32,400 30,500 31,100 31,300 31,600 34,400 37,300 40,600 43,900 Modulus (psi) Frost Line Height 30 38 38 38 38 31 34 30 32 (inches) Melt Temperature 409 442 443 443 445 404 411 405 404 (° F.) Screen Pressure (psi) 3,610 3,250 3410 3,380 3,190 3780 3850 3630 3700 Standard Output 248 249 252 252 251 250 249 250 251 (lb/hr) Frost Line Height 52 71 80 74 73 N.D. N.D. 70 69 (inches), Max Output Melt Temperature 422 460 470 463 461 N.D. 421 427 428 (° F.), Max Output Screen Pressure (psi), 3,980 4,030 4390 4,270 3,960 N.D. 4390 4090 4450 Max Output Output (lb/hr), Max Output 319 405 483 427 410 N.D. 330 389 398 *Properties of with relevant comparative examples to IE-2, each made at either 1 mil or 2 mil at a standard rate of 250 lb/hr. Note, the melt temperature, screen pressure and output were each measured at a maximum rate. N.D. = not determined

As seen in Tables 13-16, the Inventive Examples when blended with LLDPE1, have excellent output with reduced melt temperature (maximum output, shown at 10% and 20% LDPE) along with good optics/haze, dart, puncture, and tear. Thus, improved output is seen with the Inventive Examples, when blended with LLDPE1, while maintaining acceptable optics and toughness properties. Inventive polymers can be used to form films with higher output values, and comparable mechanical and optical properties. 

The invention claimed is:
 1. A composition comprising an ethylene-based polymer, which comprises the following properties: a) (Mw(abs)/Mw(conv)−2.00)*(100,000 g/mol/Mw(abs))*CDF_(IR) (MW≤10,000 g/mol)≥0.030; and b) a melt index (I2) from 0.30 to 2.50 g/10 min.
 2. The composition of claim 1, wherein the ethylene-based polymer has a CDF_(IR) (at MW≤10,000 g/mol)≥0.150.
 3. The composition of claim 1, wherein the ethylene-based polymer has a CDF_(DV) (at a MW≥1.2×10⁶ g/mol)≥0.020.
 4. The composition of claim 1, wherein the ethylene-based polymer has a CDF_(LS) (at MW≥750,000 g/mol)≥0.400.
 5. The composition of claim 1, wherein the ethylene-based polymer has Mw(conv)/Mn(conv) from 7.00 to 11.00.
 6. The composition of claim 1, wherein the ethylene-based polymer is formed in a reactor configuration comprising at least one tubular reactor.
 7. The composition of claim 1, wherein the composition further comprises another polymer different from the ethylene-based polymer.
 8. The composition of claim 1, wherein the ethylene-based polymer is a low density polyethylene (LDPE).
 9. An article comprising at least one component formed from the composition of claim
 1. 10. The article of claim 9, wherein the article is a film. 